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Electrocaloric induced retarded ferroelectric switching
Till Buchacher1,2, Maciej Rokosz1,3, Robert Dorey2,4, Jeremy Allam5 and Andrew Gregory1.
1
National Physical Laboratory, Materials Division, Teddington, TW11 0LW, UK
University of Surrey, EPSRC CDT in MiNMaT, Guildford, GU2 7XH, UK
3
Imperial College London, Department of Materials, London, SW7 2AZ, UK
4
University of Surrey, Centre for Engineering Materials, Guildford, GU2 7XH, UK
5
University of Surrey, Advanced Technology Institute, Guildford, GU2 7XH, UK
2
Ferroelectric switching in bulk materials, at modest electric fields, is a relatively fast process,
occurring on time scales of microseconds and less. A secondary retarded switching phenomenon
also occurs on time scales of seconds and has previously been attributed to defect induced elevated
energy barriers between polarisation states. As ferroelectric switching is a thermally activated
process the barrier heights are also affected by temperature which is not constant in ferroelectric
materials due to the electrocaloric effect. Here an additional EC induced retardation mechanism is
proposed whereby EC induced temperature changes repeatedly temporarily prevent further FE
switching during cooling cycles.
The electrocaloric effect recently gained a wave of interest for applications in solid state cooling,
following large effects being reported in ferroelectric thin films. [1]–[3] Electrocaloric cooling is a
promising alternative to current vapour-compression based refrigeration, combining the potential of
major energy savings with unprecedented scalability for applications even in integrated circuits.
Research on the effect however is still in its early stages. For the effect to be exploitable in
refrigeration, materials need to be optimised towards various key properties such as maximum
achievable temperature change and high cycle rates. [4] Such optimisation will require a deeper
understanding of the underlying processes that cause the effect. However at present understanding
of the electrocaloric effect is still sparse and largely based on thermodynamic approaches that focus
on macroscopic and phenomenological treatment of the effect as opposed to mechanistic
treatments. [4]–[8] Multiple authors have highlighted the weakness of this explanation and called
for a greater understanding of the fundamental theory. [9]–[12] The electrocaloric effect is generally
explained in terms of entropy changes in response to changes in the order of the material due to
changes in polarisation. [4] In a normal dielectric these changes would be attributed solely to
rearrangement of the dipoles. Ferroelectric materials however are known to have strong intrinsic
coupling between their electrical, mechanical and thermal properties, so that changes in polarisation
have not a single, but various origins and effects. [7], [8] As such one would expect the electrocaloric
effect in these materials not to have a single, but multiple contributions. Similarly it has been
previously shown that the piezoelectric response of the material contributes significantly to
observed temperature changes via the piezocaloric effect. [13]
A major contributor to polarisation changes in ferroelectrics is ferroelectric switching. The theory of
ferroelectric switching is well developed at present. Ferroelectric switching is known to be a
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thermally activated process which depends on factors intrinsic to the material, such as energy
barriers between different polarisation states, but it has also an explicit dependence on external
factors including the applied electric field and temperature. [14]–[17] An electrocaloric effect caused
by ferroelectric switching therefore would create a feedback where the temperature change
brought about by the electrocaloric effect affects the rate of ferroelectric switching and vice versa.
Similarly the electrocaloric effect has previously been shown to directly affect other properties of
ferroelectric materials. [18]
The feedback-coupling between electrocaloric effect and ferroelectric switching raises the question
as to whether the electrocaloric effect can modify ferroelectric switching rates to an extent that is
observable in the switching behaviour. Ferroelectric switching in a thin film material can occur at
pico second [19] time intervals while for bulk material it occurs on nanosecond to microsecond
timescales due to the lower breakdown strength of the materials which limits the field that can be
applied. Conversely the measurement of the electrocaloric effect relies on thermal propagation
within the material which results in a sub-second to second ‘delay’ in the measurement. However a
secondary ‘retarded’ ferroelectric switching phenomenon, occurring on time scales similar to those
of the electrocaloric effect, has also been observed. [20] This retarded switching has previously been
attributed to an inhomogeneous energy barrier landscape in the material arising from defects in the
lattice. [20] This is separate from domain wall creep which can be modelled semi-empirically using a
(E0/E)µ relationship. [21], [22] Under an applied electric field of 20 kV/cm domain wall creep would
be expected to occur at 3 µm/s where the coercive field is 10 kV/cm, µ is 0.6 [22] and the typical
energy barrier is 0.5eV. For domains on the order of 500nm in diameter (as found in these materials)
this would give a switching time in the range of 150ms which is approximately an order of
magnitude faster than the observed retardation time constants and more associated with fast
switching. For the case of an energy barrier landscape the size of the energy barriers required to
fully account for the observed degree of retardation would need to be double those of normal
switching. [16] As ferroelectric switching is known to be a thermally activated process it is possible to
offer an alternate hypothesis, which reflects the similarities in time scales, where the origins of these
elevated energy barriers are not only intrinsic to the material (e.g. energy barriers) but also a result
of temperature fluctuations, and associated changes in switching dynamics, brought about by the
electrocaloric effect.
To investigate this possible link between the electrocaloric effect and retarded ferroelectric
switching disk shaped samples 10mm in diameter and 0.5mm in thickness of soft commercial leadzirconate-titanate (PZT) near the morphotropic phase boundary (composition PZT5H), similar to
compositions in which retarded switching was observed, were used. [20] All samples were supplied
with silver electrodes fired on the two faces. Prior to the experiment the samples were fully poled by
cycling the electric field to saturation levels (figure 1b) with maximum electric field of 20 kV/cm. The
samples were then placed free standing between two brass needle contacts to avoid excessive heat
loss into the electrical connections. One electrode was connected to a high-voltage amplifier and the
other to a charge integrator with very long time constant (𝜏 > 106 𝑠). The high voltage amplifier was
used to apply a low-pass filtered step electric field from ground to 20 kV/cm to the sample. The use
of a low-pass filter allows the electric field to be applied at a controlled rate and with symmetrical
rise and fall times. The experimental apparatus is depicted in figure 1a.
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Figure 1: (a) Block diagram of the experimental apparatus. (b) Polarisation-electric field loop of the
sample at 1Hz. Indicated is the electric field and polarisation change during the experiment.
Figure 1b shows the polarisation-electric field (PE) loop of the sample recorded during poling,
showing the characteristic symmetrical shape of a soft PZT composition. Also indicated is the applied
electric field during the experiment. The field was applied in a unipolar manner from 0kV/cm to
20kV/cm and back such that the material was cycled between its remanent polarisation state Pr and
saturation polarisation Ps, without significantly altering the remanent polarisation state of the
material. Minor hysteretic loops may give rise to a temperature change but this would be positive
for both charging and discharging and would result in a gradual change in the mean temperature.
This cycle is commonly used to assess the electrocaloric effect and activates predominantly the
reversible switching contributions to polarizability while leaving the non-reversible switching
contributions unaffected. When applying or removing the electric field the electrical charge and
discharge of the sample was recorded using an oscilloscope connected to the charge integrator.
Simultaneously the temperature development on the side of the sample was recorded using a high
speed infrared camera (InfraTec ImageIR 8320 with a spectral range of 2 to 5.7 µm).
The time-dependent polarisation P(t) of the sample shows two components: a fast component, Pfast,
at the rise time of the electric field and a much slower component, Pretarded, accounting for the
retarded switching phenomenon. For each of the components there is a statistical variation, about a
mean value, of the energy barrier for switching for different regions. The retarded component of
switching can be described by a stretched exponential with a stretching exponent β. As such the
stretched exponential is a phenomenological description of processes involving a range of timescales
that can fit a wide range of phenomena over several orders of magnitude. The stretching exponent
takes values between 1 and 0 and where a value of 1 corresponds to a single, defined time constant
and small values correspond to a wide distribution of time constants. [23], [24]
For further analysis a least square algorithm was used to fit the recorded electrical behaviour with
the equation 1 for the charging transient and equation 2 for the discharging transient.
𝑃(𝑡) = 𝑃𝑓𝑎𝑠𝑡 × [1 − 𝑒
−
𝑃(𝑡) = 𝑃𝑓𝑎𝑠𝑡 × 𝑒
𝑡
𝜏𝑓𝑎𝑠𝑡
−
] + 𝑃𝑟𝑒𝑡𝑎𝑟𝑑𝑒𝑑 × [1 − 𝑒
𝑡
𝜏𝑓𝑎𝑠𝑡
+ 𝑃𝑟𝑒𝑡𝑎𝑟𝑑𝑒𝑑 × 𝑒
−(
𝑡
)𝛽
𝜏𝑟𝑒𝑡𝑎𝑟𝑑𝑒𝑑
−(
𝑡
)𝛽
𝜏𝑟𝑒𝑡𝑎𝑟𝑑𝑒𝑑
]
Equation 1
Equation 2
3
For the case of electrical charging the leakage current (obtained from linear fitting after 500s) was
subtracted from the measurement before fitting the equation. The leakage current originates
primarily from the current passing across the sample surface [20] and results in a small amount of
joule heating that manifest itself as a gradual drift in temperature over timeframes far in excess of
the characteristic retarded switching times. Some joule heating may also originate from dielectric
losses as a consequence of minor hysteresis loops during cycling. As in the case of DC leakage
current such heating would contribute to the long term change in temperature.
Figure 2 shows the electrical response and directly measured electrocaloric effect induced
temperature change during charge and discharge of the sample in response to a 20kV/cm step with
a driving field rate of 5.7MV/cm.s.
Figure 2: Electric and electrocaloric response of the sample in response to an electrical field being
applied (a) or removed (b) at a rate of 5.7MV/cm.s. The electrical response contains a fast
contribution corresponding to the RC response as well as a second ‘retarded’ contribution.
A macroscopic temperature change of 80±12mK during rise and -80±12mK during fall of the electric
field was observed on the sample. This temperature change is attributed to the electrocaloric effect
and its magnitude is in agreement with previous measurements performed on similar compositions
[6], [25]. In the electrical response the total amount of polarisation, Ptotal, shows only a minor
difference of 0.25μC between charge and discharge that can be attributed to resistive loss. The
amount of retarded switching, Pretarded, however shows a significant difference in the two cases.
Charge
(heating)
Discharge
(cooling)
Table 1: Fitting parameters of the retarded switching
Ptotal [μC] Pfast[μC]
Τfast [ms]
Pretarded [μC]
τretarded [s]
4.87±0.03 4.72±0.02 20±30
0.15±0.03
19.2±4.5
β
0.43±0.09
4.62±0.03 4.10±0.02 9±30
0.40±0.03
0.51±0.02
8.8±1.1
During charging, when the electrocaloric effect causes heating, the amount of retardation observed
is small (0.15±0.03μC). However during discharge, when the electrocaloric effect causes cooling, the
amount of retardation is a lot larger (0.51±0.02 μC). The total amount of retardation is 3% and 11%
during charge and discharge, respectively. Reflecting the dynamic nature of heat transfer within the
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system, temperature gradients may give rise to thermopolarisation effects. [26] However, such
effects would be expected to be on the order of 2-3x10-17 C for the samples in this work, which is
significantly lower than that observed here.
An alternative explanation could be gained by considering the effects of temperature on
ferroelectric switching. A decrease in temperature would make it more difficult for ferroelectric
switching to occur and would increase the level of retardation. An increase in temperature would
provide more energy to the system and would make switching more easy and would not retard the
switching at all, indicating that the retardation noted for the case of charging may be solely intrinsic
in nature. This observation indicates that a wholly thermodynamic approach with purely intrinsic
distributed energy barriers and overall temperature cannot fully explain the electrocaloric
phenomena as it would not differentiate between heating and cooling scenarios. In addition for such
a wholly thermodynamic approach, described by Arrhenius behavior, the required activation
energies would be unfeasibly large and would not correspond with the observed temperature
changes. It is proposed, instead, that much larger temperature changes are observed at a very local
scale (sub domain size) and that these temperature changes are sufficient to prevent further
switching until the local system has increased in temperature again. This allows both the observed
difference between heating and cooling as well as providing sufficiently large changes in activation
energy to prevent ferroelectric switching. Like the macroscopic EC effect the proposed large
temperature changes are a result of significant entropy changes brought by local ferroelectric
switching. Corresponding macroscopic ‘giant’ EC effects are not observed due to the self-terminating
nature of the effect.
The time constants for the retarded switching are longer than would be expected (< 1s) if the
retarded switching were controlled by thermal diffusion time (𝑑2 /𝛼 where 𝑑 = 0.5𝑚𝑚 is the
thickness and 𝛼 = 4 × 10−7 𝑚2 /𝑠 [27] is the diffusivity). Instead a stop-start type of relaxation type
behavior may occur whereby some switching would initially occur thereby preventing further
switching due to the local cooling. On warming, controlled by thermal diffusion, further switching
would occur only for it to cause a re-freezing of the system. These continued lock-unlock cycles
would result a time constant that is longer than that associated with thermal diffusion on its own.
If a correlation does exist between the electrocaloric effect and retarded switching both phenomena
should share similar behaviour in response to external driving conditions. The electrocaloric effect is
known to scale with temperature, reaching its maximum values in the vicinity of the Curie
temperature. [28] The electrocaloric effect is also known to have a strong dependence on the driving
electric field rate. [29] While some consider the origin of the driving rate dependence to be due to
adiabatic conditions only occurring at switching times less than thermal transit times, Rose et al.
postulated a link between this dependence on driving field rate and the occurrence of a large
electrocaloric effect via ferroelectric switching. [2]
Being a thermally activated process ferroelectric switching is not retarded by the increase in
temperature during the charge/heating cycle. However the temperature drop during the
discharge/cooling cycle does cause retardation. Therefore further investigations to explore this
relationship focused on the discharge/cooling cycle.
Figure 3a shows the magnitudes of retarded switching and macroscopic electrocaloric effect for
various sample temperatures. In this case the magnitude of the electrocaloric effect was determined
5
indirectly via the Maxwell relation (𝜕𝑃/𝜕𝑇)𝐸 = (𝜕𝑆/𝜕𝐸) 𝑇 from PE loops recorded at 1Hz (i.e.
capturing both fast and retarded signals) which is a common method. [8] The indirect route for
determining temperature was chosen in this instance as it provides a high accuracy measure of the
average volumetric temperature as opposed to the less accurate measure of surface temperature
that could be determined experimentally. In our case the magnitude of the electrocaloric effect at
room temperature measured by the indirect method is in good agreement with that measured
directly. Both, the amplitudes of the electrocaloric effect and the retarded switching increase in a
similar manner with temperature indicating good correlation.
Figure 3: Magnitude of retarded switching and magnitude of indirectly calculated electrocaloric
effect for various temperatures (a) and amplitude of directly measured electrocaloric effect for
multiple driving field rates (b). Below 100𝑘𝑉/(𝑐𝑚 ∙ 𝑠) a linear ramp was used, as these ramp times
were outside of the linear response of the low pass filter used.
Figure 3b shows direct measurements of the electrocaloric effect and amplitude of retarded
switching for various driving field rates. Both temperature changes and switching would be expected
to be limited by the ability of acoustic phonons to propagate through the material. As such it would
be expected that, in cases where EC temperature changes originate only from switching, no
temperature changes would saturate at ramp rates corresponding to those faster than the phonon
propagation velocity. In this work that would correspond to a driving field rate of 400kVcm-1s-1. This
is only partially observed in figure 3b due to the high degree of uncertainty in the experimental
results but could also indicate that the EC effect is not directly controlled by phonon propagation.
The charge and discharge behaviour, temperature dependence and driving field rate dependence all
show a correlation between the amplitudes of the electrocaloric effect and the retarded switching
that is consistent with a common origin. This origin cannot be a uniform temperature change
brought about by dipole rearrangement and the piezocaloric effect as these are intrinsically much
faster processes that would not be altered at the driving field rates used in this experiment.
Furthermore the asymmetry of the retarded switching in the charge and discharge behaviour cannot
be accounted for by a distributed energy barrier model but instead can be explained by a model
incorporating significant localised temperature fluctuations. The temperature changes required to
cause this form of retardation are on the scale of multiple K however this is at odds with the
recorded mK-level of fluctuations observed in the bulk material. This could be accounted for by
considering the different length scales of the effect and observation: A large electrocaloric effect due
to ferroelectric switching has to occur very localised – on the order of unit cells and individual
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domains – while the bulk electrocaloric effect is a macroscopic property observed after thermal
diffusion has occurred and as such would be expected to be lower in magnitude.
A large, localised electrocaloric effect due to ferroelectric switching would inhibit further switching
locally until sufficient temperature diffusion has occurred to an extent that switching occurs again.
This self-inhibiting nature would create a cascading effect where temperature due to electrocaloric
effect and switching keep one-another in equilibrium for an extended period of time leading to
retarded FE switching on time scales of associated with thermal conductivity. Preliminary finite
difference modelling of this phenomenon suggest that temperature fluctuations of 25K within a
volume around 10 μm in diameter would be required to account for the observed behaviour. If the
volume were smaller the temperature change would be larger. Such a temperature fluctuation is
within the bounds of the maximum theoretical ECE temperature fluctuations as predicted by Pirc et
al. [30] However, additional work would be required to experimentally verify that such a
temperature gradient could be maintained over the required time frame to explain the current
observations.
The proposed localised occurrence of the ferroelectric switching induced electrocaloric effect and
the resulting temperature induced stresses in the material could also help in the understanding of
other phenomena related to ferroelectric and electrocaloric materials. In particular this may also
help explain some of the observed fatigue behaviour of ferroelectrics with agglomeration of point
defects and mechanical damage in form of microcracking which could be triggered by large stress
gradients introduced by large local temperature variations within the material. [31]
While we acknowledge that the phenomenon may be caused by other effects the observed
correlation in FE switching and EC behaviours, and the asymmetry between heating and cooling,
make it highly likely that the phenomenon is caused by a large, localised electrocaloric effect due to
ferroelectric switching. In line with Liu et al.’s recent review [12], we hope to encourage the
community to think of the electrocaloric effect not solely in terms of simplified thermodynamic
models and hope to stimulate further discussion of the topic to develop a truly dynamic model of
the electrocaloric effect.
Acknowledgements
The financial support of the UK’s Engineering and Physical Sciences Research Council via the Centre
for Doctoral Training in Micro and Nano Materials and Technology at the University of Surrey and
the UK’s National Measurement Office is gratefully acknowledged. M.Rokosz was additionally
supported by a scholarship under the UK’s Partner Research Institution (PRI) Scheme. The data is
freely available at https://doi.org/10.5281/zenodo.200505
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